Primary Observables for Indirect Searches at Colliders

Abstract

We consider the complete set of observables for collider searches for indirect effects of new heavy physics. They consist of $SU(3{)}_{\mathrm{C}}\times U(1{)}_{\mathrm{EM}}$ invariant interaction terms/operators that parameterize deviations from the Standard Model. We show that, under very general assumptions, the leading deviations from the Standard Model are given by a finite number of `primary' operators, with the remaining operators given by `Mandelstam descendants' whose effects are suppressed by powers of Mandelstam variables divided by the mass scale $M$ of the heavy physics. We explicitly determine all 3 and 4-point primary operators relevant for Higgs signals at colliders by using the correspondence between on-shell amplitudes and independent operators. We give a detailed discussion of the methods used to obtain this result, including a new analytical method for determining the independent operators. The results are checked using the Hilbert series that counts independent operators. We also give a rough sketch of the phenomenology, including unitarity bounds on the interaction strengths and rough estimates of their importance for Higgs decays at the HL-LHC. These results motivate further exploration of Higgs decays to $Z\bar{f}f$, $W\bar{f}{f}^{\prime }$, $\gamma \bar{f}f$, and $Z\gamma \gamma$.

Comments: 46 pages, 2 figures, 13 tables. Final published version in JHEP